An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).     

Modelling and comparative study of viscoelastic laminated composite beam – an operator based finite element approach

Mechanics of Time-Dependent Materials - Finite element formulation of damped laminated composite beam considering both Euler-Bernoulli and Timoshenko beam theory is proposed based on Equivalent...     

Shape control of smart composite plate with non-rectangular piezoelectric actuators

Quasi-static shape control of a smart structure may be achieved through optimizing the applied electric fields, loci, shapes and sizes of piezoelectric actuators attached to the structure. In this paper, a finite element analysis (FEA) software has been developed for analyzing static deformation of smart composite plate structures with non-rectangular shaped PZT patches as actuators. The mechanical deformation of the smart composite plate is modeled using a 3rd order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation is verified by comparing with experimentally measured deformation. Numerical results are obtained for the optimum values of the electric field in the PZT actuators to achieve the desired shape using the linear least square (LLS) method. The numerical results demonstrate the influence of the shapes of actuators.     

On the response of a timoshenko beam under initial stress to a moving load

When an axial compressive force is present, the wavelength of the propagating free waves in a beam rapidly decreases. The conventional Euler-Bernoulli beam equations are often not adequate for determining dynamic behavior of the moving load on a beam supported on an elastic foundation when initial axial stress is present. Equations derived by Sun for the Timoshenko beam with initial axial stress (based on Trefftz's theory), form the basis of this investigation. Analytical solutions are presented for deformations of the beam both with and without damping. Expressions of the critical velocity as a function of initial axial stress and foundation modulus parameters, are obtained for the Timoshenko beam. Critical velocities of the Timoshenko beam, with and without axial stress, are compared with that obtained using Euler-Bernoulli beam formulation. Some significant agreements and disagreements in the behaviors of the two systems are described.     

利用压电自传感驱动器进行裂纹钢梁损伤识别的实验研究

压电陶瓷是一种智能材料，可以在结构健康监测系统中同时用作传感器和驱动器。基于压电阻抗的损伤识别技术的基本原理，对裂纹钢梁进行了损伤识别和定位的实验研究。将三片压电陶瓷（PZT）粘贴在钢梁表面的不同部位作为驱动器和传感器，通过测量梁损伤前后压电陶瓷片的电阻抗变化来识别梁中的裂纹损伤。从导纳（阻抗的倒数）幅值谱曲线中提取裂纹梁的反谐振频率，通过比较各压电片位置的反谐振频率变化识别了裂纹位置；同时比较不同损伤工况下的反谐振频率变化定性地识别裂纹梁结构的损伤程度。     

Reddy高阶组合梁的非线性有限元分析

该文基于Reddy高阶梁理论,提出了小变形双层组合梁的隐式运动学假定;应用拉格朗日乘子法,将该隐式关系引入到组合梁的最小势能原理,得到了考虑各子梁和粘结滑移层非线性材料特性的高阶组合梁非线性位移法有限单元,且该单元可以容易地转化为非线性Timoshenko和Euler-Bernoulli组合梁有限单元。随后,该研究分别应用提出的Reddy、Timoshenko和Euler-Bernoulli组合梁有限单元对双跨连续钢-混凝土组合梁进行了准静力分析,考察剪切效应对组合梁构件的挠度、粘结层滑移和截面应力的影响,且参数分析了组合梁的跨高比对剪切效应的影响。参数分析表明：短粗组合梁结构往往表现出显著的剪切效应,Newmark假定不再适用。     

Timoshenko梁功率流主动控制研究

为了研究扰动影响下梁式结构的动力学响应与主动控制,首先基于Timoshenko梁理论,采用行波方法建立了悬臂梁结构的动力学模型并获得了其在扰动下的精确动力学响应,进一步得到结构中传播的功率流,并以此为目标函数,优化得到了最优控制力的大小与相位,然后对结构施加最优控制力,实现了Timoshenko梁结构的功率流主动控制。对Timoshenko梁结构动力学响应与功率流主动控制方法进行了数值计算,并与Euler-Bernoulli梁理论计算结果进行了对比分析。结果表明：采用行波方法计算梁结构的动力学响应准确可靠;Timoshenko梁模型较Euler-Bernoulli梁模型在中、高频段更为精确,且更接近工程实际;通过数值计算与分析验证了基于行波方法功率流主动控制的正确性与有效性,并且功率流主动控制可以明显降低梁式结构全频域内的抖动。     

大挠度梁静态变形对动态特性影响分析

在经典梁理论基础上，引入剪切修正因子，采用U.L法，推导了新的空间大挠度梁的切线刚度矩阵；以三维连续体增量虚功原理为基础，建立了空间大挠度梁考虑剪切影响的静态分析模型和动态特性分析模型；首先根据所建立的模型进行了大挠度梁的静态特性分析，验证了模型的正确性；然后进行了大挠度梁的动态特性分析，揭示了悬臂梁静态大变形对动态特性的影响规律。指出悬臂梁在大载荷作用下，结构固有频率会因为梁的大变形而发生明显变化，基频变化尤为明显。     

Adhesive element modelling and weighted static shape control of composite plates with piezoelectric actuator patches

A novel finite element model is presented for static and dynamic analysis of composite plates integrated with a laminated piezoelectric layer, a host laminated composite plate and an adhesive layer between them. A new adhesive element is developed which includes both peel and shear effects in the adhesive layer based on first‐order shear deformation plate theory. The thin adhesive layer between the piezoelectric layer and the host plate is modelled by assuming that it carries constant shear and peel strains throughout its thickness. In addition, a weighted static shape control scheme for finding the optimal voltage distribution for static shape control is given. By selecting different weighting matrices, a variety of items such as displacements, slopes, curvatures, strains and even generalized forces, can be included in finding the optimal actuating voltage for static shape control. The present model is validated by comparing with those results available in the literature. The numerical results show that the weighted linear least method can give a satisfactory voltage distribution to best match the desired shape. Copyright © 2004 John Wiley & Sons, Ltd.     

Identification of delamination in a composite beam using integrated piezoelectric sensor/actuator layer

This paper describes the use of an integrated piezoelectric sensor/actuator (IPSA) layer to detect a delamination in a laminated composite beam by monitoring the sensor charge output (SCO) distributions along the beam of the first three order frequencies. For the sake of predicting the first three order frequencies and SCO distributions using the IPSA layer, a model-based delamination detection approach is presented. The corresponding dynamic analytical model that includes parameters characterizing delamination is developed using the classical beam theory and the assumption of constant peel and shear strains through the bond line thickness in bonded joint. Using the present analytical model, the effects of delamination length l_d, delamination gap t_g, actuator segment length l_a, actuator segment location X_a and electric field E on the SCO values are discussed. Finally, a comparison of the first three order frequencies between the present analytical and finite element analysis (FEA) models reveals that there is good agreement between these two models.     

Transverse Shear and Normal Deformation Theory for Bending Analysis of Laminated and Sandwich Elastic Beams

The influence of transverse normal strain on bending analysis of cross-ply laminated and sandwich beams is presented. A higher-order shear deformation beam theory is developed. Euler-Bernoulli classical, Timoshenko first-order and simple higher-order theories have been also used in the analysis. The governing equations for a beam composed of orthotropic layers and subjected to any given mechanical load distribution are derived. Making use of Navier-like approach, exact solutions are obtained for cross-ply laminated and sandwich beams subjected to arbitrary loadings. Numerical results for beams with the simply-supported boundary conditions are presented. The effects due to transverse normal strain, transverse shear deformation and number of layers on the static response of the beams are investigated.     

Shape control and damage identification of beams using piezoelectric actuation and genetic optimization

This paper deals with the shape control of beams under general loading conditions, using piezoelectric patch actuators that are surface bonded onto beams to provide the control forces. The mathematical formulation of the model is based on the shear deformation beam theory (Timoshenko theory) and the linear theory of piezoelectricity. The numerical solution of the model is based on the development of superconvergent (locking-free) finite elements using the form of the exact solution of the Timoshenko beam theory and Hamilton’s principle. The optimal values for the locations of the piezo-actuators are determined and optimal voltages for shape control are obtained for cantilever beams by using a genetic optimization procedure. Finally, a simplified related damage identification problem is formulated and solved using static data and genetic optimization.     

On the dynamic behaviour of the Timoshenko beam finite elements

First, various finite element models of the Timoshenko beam theory for static analysis are reviewed, and a novel derivation of the 4 × 4 stiffness matrix (for the pure bending case) of the superconvergent finite element model for static problems is presented using two alternative approaches: (1) assumed-strain finite element model of the conventional Timoshenko beam theory, and (2) assumed-displacement finite element model of a modified Timoshenko beam theory. Next, dynamic versions of various finite element models are discussed. Numerical results for natural frequencies of simply supported beams are presented to evaluate various Timoshenko beam finite elements. It is found that the reduced integration element predicts the natural frequencies accurately, provided a sufficient number of elements is used. The research reported herein is supported by theOscar S. Wyatt Endowed Chair.     

Shear coefficients for thin-walled composite beams

The shear coefficient in Timoshenko beam theory is obtained for thin-walled beams constructed of laminated panels of composite material using a variation of the method due to Cowper. Formulae are presented for a class of such composite beams. Comparisons are made with Cowper's original formulae for the case of an isotropic beam. The effect of shear deformation under static loading of typical composite beams is investigated. A procedure is outlined for the distribution of plies in the laminated panels to achieve optimal response under static or dynamic loading.     

Spectral element model for axially loaded bending–shear–torsion coupled composite Timoshenko beams

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide extremely accurate solutions, while reducing the total number of degrees-of-freedom to resolve the computational and cost problems. Thus, in this paper, the spectral element model is developed for an axially loaded bending–shear–torsion coupled composite laminated beam which is represented by the Timoshenko beam model based on the first-order shear deformation theory. The high accuracy of the spectral element model is then numerically verified by comparing with exact theoretical solutions or the solutions obtained by conventional finite element method. For the numerical verification, the finite element model is also provided for the composite laminated beam.     

层合梁的弯曲与自由振动分析

本文在铁摩辛柯梁理论的基础上, 应用迭合刚度的方法和Hamilton原理, 导出了适合于层合梁静力分析和动力分析的控制方程组(在单层情况下, 将退化成Timoshenko梁的方程)及边界条件。而且, 利用所获得的控制方程, 求得了层合梁一些问题的解析解及相应的数值结果。      

Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams

This paper presents a new finite element formulation, referred to as reference surface element (RSE) model, for numerical prediction of dynamic behaviour of delaminated composite beams and plates using the finite element method. The RSE formulation can be readily incorporated into all elements based on the Timoshenko beam theory and the Reissner–Mindlin plate theory taking into account the transverse shear deformations. The ‘free model' and ‘constrained model' for dynamic analysis of delaminated composite beams and/or plates have been unified in this RSE formulation. The RSE formulation has been applied to an existing 2-node Timoshenko beam element taking into account the transverse shear deformations and the bending–extension coupling. Frequencies and vibration mode shapes are determined through solving an eigenvalue problem. Numerical results show that the present RSE model is reliable and practical when used to predict frequencies and mode shapes of delaminated composite beams. The RSE formulation has also been used to investigate the effects of the number, size and interfacial loci of delaminations on frequencies and mode shapes of composite beams.     

On the effects of higher vibration modes in the analysis of three point bend testing

Influence of higher modes of vibration in the dynamic analysis of impact three point bend specimen based on Euler-Bernoulli and Timoshenko beam theories are investigated in an attempt to predict the oscillatory behavior seen in the measured dynamic SIF history. Forced vibration of the cracked beam is analyzed by normal mode summation method. Contact force history computed using fundamental mode approximation is applied as input forcing function and the computed SIF histories are compared with finite element model and experimental data. Analytical and finite element results show that modes higher than the third have practically no influence on the notched beam response.     

A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates

A new 4-node quadrilateral finite element is developed for the analysis of laminated composite plates containing distributed piezoelectric layers (surface bonded or embedded). The mechanical part of the element formulation is based on the first-order shear deformation theory. The formulation is established by generalizing that of the high performance Mindlin plate element ARS-Q12, which was derived based on the DKQ element formulation and Timoshenko’s beam theory. The layerwise linear theory is applied to deal with electric potential. Therefore, the number of electrical DOF is a variable depending on the number of plate sub-layers. Thus, there is no need to make any special assumptions with regards to the through-thickness variation of the electric potential, which is the true situation. Furthermore, a new “partial hybrid”-enhanced procedure is presented to improve the stresses solutions, especially for the calculation of transverse shear stresses. The proposed element, denoted as CTMQE, is free of shear locking and it exhibits excellent capability in the analysis of thin to moderately thick piezoelectric laminated composite plates.     

不同梁理论之间简支梁特征值的解析关系

利用Euler-Bernoulli梁理论(EBT)、Timoshenko梁理论(一阶理论,TBT)和Reddy三阶梁理论(RBT)之间,梁的特征值问题在数学上的相似性,研究了不同梁理论之间特征值的关系。将特征值问题的求解转化为一个代数方程的求解,并导出了不同梁理论之间梁的特征值之间的精确解析关系。因此,只要已知梁的经典结果(临界载荷和固有频率),便很容易从这些关系中获得一阶和三阶梁理论下的相应结果。另外,从这些关系中获得的含有剪切变形影响的结果,可以用于检验一阶和三阶梁理论下梁数值结果的有效性、收敛性以及精确性等问题。